diff --git a/src/spanningtrees/kruskal.jl b/src/spanningtrees/kruskal.jl
index 52cb936ae..883e39495 100644
--- a/src/spanningtrees/kruskal.jl
+++ b/src/spanningtrees/kruskal.jl
@@ -1,5 +1,5 @@
 """
-    kruskal_mst(g, distmx=weights(g); minimize=true)
+	kruskal_mst(g, distmx=weights(g); minimize=true)
 
 Return a vector of edges representing the minimum (by default) spanning tree of a connected, 
 undirected graph `g` with optional distance matrix `distmx` using [Kruskal's algorithm](https://en.wikipedia.org/wiki/Kruskal%27s_algorithm).
@@ -15,6 +15,7 @@ function kruskal_mst end
     connected_vs = IntDisjointSets(nv(g))
 
     mst = Vector{edgetype(g)}()
+    nv(g) <= 1 && return mst
     sizehint!(mst, nv(g) - 1)
 
     weights = Vector{T}()
diff --git a/src/steinertree/steiner_tree.jl b/src/steinertree/steiner_tree.jl
index 6f7713cd1..9676b9ae6 100644
--- a/src/steinertree/steiner_tree.jl
+++ b/src/steinertree/steiner_tree.jl
@@ -1,5 +1,5 @@
 """
-    filter_non_term_leaves!(g, term_vert)
+	filter_non_term_leaves!(g, term_vert)
 
 Remove edges of `g` so that all non-isolated leaves of `g` are in the set `term_vert`
 """
@@ -44,6 +44,8 @@ function steiner_tree end
     g::AG::(!IsDirected), term_vert::Vector{<:Integer}, distmx::AbstractMatrix{U}=weights(g)
 ) where {U<:Real,T,AG<:AbstractGraph{T}}
     nvg = nv(g)
+    length(term_vert) == 0 && return SimpleGraph{T}()
+    length(term_vert) == 1 && return SimpleGraph{T}(first(term_vert))
     term_to_actual = T.(term_vert)
     unique!(term_to_actual)
 
diff --git a/test/spanningtrees/kruskal.jl b/test/spanningtrees/kruskal.jl
index b45eb8cb6..ddf8fead8 100644
--- a/test/spanningtrees/kruskal.jl
+++ b/test/spanningtrees/kruskal.jl
@@ -44,4 +44,13 @@
         @test sort([(src(e), dst(e)) for e in mst2]) == sort([(src(e), dst(e)) for e in vec2])
         @test sort([(src(e), dst(e)) for e in max_mst2]) == sort([(src(e), dst(e)) for e in max_vec2])
     end
+
+    # non regression test for #362
+    g = Graph()
+    mst = @inferred(kruskal_mst(g))
+    @test isempty(mst)
+
+    g = Graph(1)
+    mst = @inferred(kruskal_mst(g))
+    @test isempty(mst)
 end
diff --git a/test/steinertree/steiner_tree.jl b/test/steinertree/steiner_tree.jl
index c5ee13b90..35bd323dd 100644
--- a/test/steinertree/steiner_tree.jl
+++ b/test/steinertree/steiner_tree.jl
@@ -19,6 +19,10 @@
         g_copy = SimpleGraph(g)
         Graphs.filter_non_term_leaves!(g_copy, [2, 5])
         @test ne(g_copy) == 2 # [Edge(2, 1), Edge(1, 5)]
+
+        # non regression test for #362
+        g_st = @inferred(steiner_tree(g, [2]))
+        @test ne(g_st) == 0
     end
 
     g4 = path_graph(11)